Image-pickup optical system and image pickup apparatus

ABSTRACT

An image-pickup optical system includes: a first lens provided near an aperture stop and configured to correct aberration; and a second lens arranged between the first lens and an image sensor and configured to collect light, the first lens being a gradient index lens. The degree of freedom of design of a gradient index lens is higher than that of a lens having a constant refractive index, and a gradient index lens thus has a high potential as a device for a lens. Because such a gradient index lens is employed, it is possible to correct aberration without performing expensive processing such as polishing for example. In other words, as a result, costs may be reduced and image-forming properties may not be reduced at the same time.

CROSS REFERENCE PARAGRAPH

The present application is a continuation application of U.S. patentapplication Ser. No. 14/399,045, filed Nov. 5, 2014, which is a NationalStage Entry of PCT/JP2013/002515, filed Apr. 12, 2013, and claims thebenefit of priority from prior Japanese Patent Application JP2012-112423, filed May 16, 2012, the entire content of which is herebyincorporated by reference. Each of the above-referenced applications ishereby incorporated herein by reference in its entirety.

TECHNICAL FIELD

The present technology relates to an image-pickup optical systemconfigured to form images to detect images, and an image pickupapparatus employing the image-pickup optical system.

BACKGROUND ART

Image-pickup optical systems, which are used not only for thevisible-light range but also for the infrared-frequency range or theterahertz-frequency range, have been developed as image-pickup opticalsystems configured to detect images.

For example, an infrared image-pickup optical system uses heat from anobject such as a person or an animal, i.e., far-infrared (wavelength 8μm to 12 μm), and is used to pick up an image in a dark place, toobserve a temperature distribution, or the like.

Moreover, an image-pickup optical system for the terahertz wave(wavelength 30 μm to 3 mm: 100 GHz to 10 THz) is used for so-callednon-destructive tests such as for example security checks at airportfacilities.

Patent Document 1: Japanese Patent Application Laid-open No. 2010-526318

Patent Document 2: Japanese Patent Application Laid-open No. 2011-82324

Patent Document 3: Japanese Patent Application Laid-open No. 2010-527565

Patent Document 4: Japanese Patent Application Laid-open No. 2008-507733

SUMMARY OF INVENTION Problem to be Solved by the Invention

Here, it is desirable that the above-mentioned image-pickup opticalsystems configured to pick up infrared images or terahertz-wave imagesshould be high-resolution in order to pick up clear images.

It is desirable to reduce various kinds of optical aberration to makeresolution high.

However, few lens materials may be used from the viewpoints oftransmittance and the like for the infrared wavelength range and theterahertz-wave wavelength range, and it is difficult to process suchlens materials, which are problematic.

For example, germanium and the like are known as materials havingrelatively high infrared transmittance. However, those lens materialshaving high infrared transmittance are relatively high in hardness, andit is difficult to process those lens materials.

It is difficult to reduce costs because for example it takes a long timeto process them. Specifically if an aspheric shape is processed(polished) to correct aberration, it is necessary to use a precisionequipment and to process it for a long time, which results inunavoidable high costs.

The present technology has been made in view of the above-mentionedproblems. It is an object of the present technology to reduce costs ofan image-pickup optical system, which forms images to especially pick upinfrared images or terahertz-wave images, and to prevent image-formingproperties from being decreased at the same time.

Means for Solving the Problem

According to the present technology, an image-pickup optical system isstructured as follows to solve the above-mentioned problems.

In other words, an image-pickup optical system according to the presenttechnology includes a first lens provided near an aperture stop andconfigured to correct aberration.

The image-pickup optical system further includes a second lens arrangedbetween the first lens and an image sensor and configured to collectlight.

Moreover, the first lens is a gradient index lens.

Moreover, according to the present technology, an image pickup apparatusis structured as follows.

In other words, an image pickup apparatus according to the presenttechnology includes the image-pickup optical system of the presenttechnology; an image detector configured to detect an image formed bythe image-pickup optical system; and an image-signal obtaining unitconfigured to obtain an imaging signal based on a detection signal fromthe image detector.

Here, the degree of freedom of design of a gradient index lens is higherthan that of a lens having a constant refractive index, and a gradientindex lens thus has a high potential as a device for a lens. Accordingto the present technology employing such a gradient index lens, it ispossible to correct aberration without performing expensive processingsuch as polishing for example. In other words, as a result, costs may bereduced and image-forming properties may not be reduced at the sametime.

Effect of the Invention

According to the present technology, costs of an image-pickup opticalsystem configured to form images to pick up images, i.e., specifically,an infrared or terahertz-wave image-pickup optical system, may bereduced, and image-forming properties may not be reduced at the sametime.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 A block diagram showing the internal structure of an image pickupapparatus of an embodiment.

FIG. 2 A diagram illustrating the outline of the structure of theimage-pickup optical system of the embodiment.

FIGS. 3A and 3B The diagrams showing an example of a refractive indexdistribution pattern in the radius direction to be prepared in order tocorrect spherical aberration.

FIGS. 4A and 4B Each shows an example of the structure of a unit cell ofa metamaterial.

FIG. 5 A diagram showing the structure of a metamaterial.

FIGS. 6A and 6B Diagrams showing a method of giving a refractive indexdistribution to a metamaterial lens.

FIG. 7 A diagram showing measurement results of refractive indexes whenthe length of cross-shaped arms of a cross-shaped conductor is changed.

FIG. 8 A diagram showing the structure of an image-pickup optical systemof Example 1.

FIG. 9 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 1 in the radiusdirection.

FIG. 10 A diagram showing resolution properties (MTFs) of theimage-pickup optical system of Example 1 at the respective image heights(0.0 mm, 1.5 mm, and 3.5 mm).

FIG. 11 A diagram showing the structure of an image-pickup opticalsystem of Example 2.

FIG. 12 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 2 in the radiusdirection.

FIG. 13 A diagram showing resolution properties (MTFs) of theimage-pickup optical system of Example 2 at the respective image heights(0.0 mm, 1.5 mm, and 3.5 mm).

FIG. 14 A diagram showing the structure of an image-pickup opticalsystem of Example 3.

FIG. 15 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 3 in the radiusdirection.

FIG. 16 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 3 in theoptical-axis direction.

FIG. 17 A graphic diagram showing second order differential of therefractive index distribution of a second lens of Example 3 in theoptical-axis direction.

FIG. 18 A diagram showing resolution properties (MTFs) of theimage-pickup optical system of Example 3 at the respective image heights(0.0 mm, 1.5 mm, and 3.5 mm).

FIG. 19 A diagram showing the structure of an image-pickup opticalsystem of Example 4.

FIG. 20 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 4 in the radiusdirection.

FIG. 21 A diagram showing resolution properties (MTFs) of theimage-pickup optical system of Example 4 at the respective image heights(0.0 mm, 1.5 mm, and 3.5 mm).

FIG. 22 A diagram showing the structure of an image-pickup opticalsystem of Example 5.

FIG. 23 A graphic diagram showing second order differential of therefractive index distribution of a first lens of Example 5 in the radiusdirection.

FIG. 24 A diagram showing resolution properties (MTFs) of theimage-pickup optical system of Example 5 at the respective image heights(0.0 mm, 1.5 mm, and 3.5 mm).

MODES FOR CARRYING OUT THE INVENTION

Hereinafter, embodiments of the present technology will be described.

Note that description will be made in the following order.

<1. Image pickup apparatus and image-pickup optical system ofembodiment>

[1-1. Structure of image pickup apparatus]

[1-2. Outline of image-pickup optical system of embodiment]

<2. Specific examples>

[2-1. Example 1]

[2-2. Example 2]

[2-3. Example 3]

[2-4. Example 4]

[2-5. Example 5]

<3. Modification examples>

1. Image Pickup Apparatus and Image-Pickup Optical System of Embodiment1-1. Structure of Image Pickup Apparatus

FIG. 1 is a block diagram showing the internal structure of an imagepickup apparatus 1 of an embodiment.

Firstly, it is presupposed that the image pickup apparatus 1 of thisembodiment is an infrared image pickup apparatus configured to pick upinfrared images.

As shown in FIG. 1, the image pickup apparatus 1 includes an opticalblock 2, an image sensor (imager) 3, an image-signal obtaining unit 4,and an image signal processor 5.

The optical block 2 inclusively shows a below-mentioned image-pickupoptical system of the embodiment. The optical block 2 collects infraredlight (infrared) from an object-of-imaging (object), which is denoted byincident light Li in the figure, on an imaging plane (image plane) ofthe image sensor 3.

The image sensor 3 detects the infrared collected by the optical block2, and obtains infrared detection signals depending on theabove-mentioned infrared from the object-of-imaging.

An example of infrared detection devices of the image sensor 3, whichare configured to obtain infrared detection signals, are devicesincluding pyroelectric devices. Alternatively, thermopile infrareddetection devices, to which thermocouples generating Seebeck effect areconnected, bolometric infrared detection devices, which utilize changein resistance values resulting from increase in temperature, or the likemay be used.

Note that the infrared detection devices are not limited to them, andany kind of infrared detection devices may be used as long as it ispossible to detect infrared.

Note that, if pyroelectric devices are used as infrared detectiondevices, a shutter is provided to periodically block infrared light,which enters the image sensor 3. This is to support the fact that apyroelectric device is not a device which outputs values correspondingto temperature per se but a device which outputs values corresponding totemperature differences (temperature changes). In other words, theabove-mentioned shutter periodically generates the irradiationstatus/blocked status of infrared light, and temperature difference isthus generated purposefully. As a result, an image (infrared-takenimage) having an appropriate temperature distribution of a static objectmay be obtained.

The image-signal obtaining unit 4 inputs infrared detection signals(detection signals obtained by the above-mentioned infrared detectiondevices) obtained by the image sensor 3, and obtains infrared-imagingsignals.

The image signal processor 5 performs various kinds of image-signalprocessing on the imaging signals obtained by the image-signal obtainingunit 4. For example, black level correction, pixel defect compensation,aberration correction, optical shading correction, lens distortioncorrection, temperature adjustment, calculation of an amount of distancechange, coding, and the like are performed.

Output from the image signal processor 5 is sent to an external display(image display apparatus) or the like of the image pickup apparatus viaa not-shown interface and the like.

1-2. Outline of Image-Pickup Optical System of Embodiment

FIG. 2 is a diagram illustrating the outline of the structure of theimage-pickup optical system of the optical block 2 of the embodiment.

In FIG. 2 and in addition the below-mentioned structure diagrams (FIGS.8, 11, 14, 19, and 22) of the optical system, it is assumed that animaging-target object is arranged at the left side of the sheet. Inother words, the left side of the sheet is the object side, and theright side of the sheet is the image plane side.

Note that FIG. 2 shows the structure of the image-pickup optical systemand in addition the above-mentioned image sensor 3 of FIG. 1.

As shown in the figure, in the image-pickup optical system of theembodiment, an aperture stop 10, a first lens 11, a second lens 12, anda sensor window 13 are arranged from the object side to the image planeside.

The first lens 11 is a lens configured to correct aberration, and isprovided in the vicinity of the aperture stop 10. Because the first lens10 is arranged in the vicinity of the aperture stop 10 as describedabove, spherical-aberration correction effect is increased.

Further, the second lens 12 functions as a collective lens configured tocollect infrared light passing through the first lens 11. In otherwords, the second lens 12 functions as an imaging lens, which forms aninfrared image on an imaging plane of the image sensor 3.

The sensor window 13 has, for example, a flat plate shape, and isprovided to protect the imaging plane of the image sensor 3.

Here, in the image-pickup optical system of this embodiment, at leastthe first lens 11 is a gradient index lens (so-called GRIN lens).

The degree of freedom of design of a GRIN lens is higher than that of alens having a constant refractive index, and a GRIN lens thus has a highpotential as a device for a lens.

Because such a GRIN lens is used as the first lens 11, it is notnecessary to perform expensive processing for aberration correction asin the past, and the costs may be reduced from this viewpoint.

Moreover, in the image-pickup optical system of this embodiment, thefocal distance f₂ of the second lens 12 is approximately the same as thefocal distance f of the entire image-pickup optical system including thesecond lens 12.

Specifically, for example the image-pickup optical system is designedsuch that the following condition is satisfied.

$\begin{matrix}{0.9 \leq \frac{f_{2}}{f} \leq 1.1} & \left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack\end{matrix}$

The fact that the focal distance f₂ of the second lens 12 isapproximately the same as the focal distance f of the entireimage-pickup optical system means that the second lens 12 has almost allof the light-collection function of the optical system, and it is notnecessary for the first lens 11 side to have a light-collectionfunction. In other words, because of this, it is possible to design thefirst lens 11 as a lens specialized in aberration correction, and as aresult it is possible to increase an aberration-correction effect.

Moreover, in this embodiment, the refractive index distribution(hereinafter referred to as refractive index distribution N₁) of thefirst lens 11 being a GRIN lens is designed such that second orderdifferential in its radius direction increases monotonically.

Here, the refractive index distribution N of the GRIN lens is asfollows.N=N ₀ +nr ₁₂ ·R ² +nr ₁₄ ·R ⁴ +nr ₁₆ ·R ⁶ +nz ₁₁ ·

+nz ₁₂·

² +nz ₁₃·

³  [Math. 2]where N₀ is a standard refractive index of a GRIN lens, R is theposition of the lens in the radius direction (center of optical axis ofincident plane is 0), and Z is the position of the lens in theoptical-axis direction (center of optical axis of incident plane is 0)in [Math. 2]. Moreover, nr_(ij) is a coefficient of the term Rj, andnz_(ij) is a coefficient of the term Z_(j).

Note that, here, for simplicity, the sextuplicate term R and the lowerand the cubed term Z and the lower are shown, but the same applies tohigher-order terms. With regard to the refractive index distribution Nof a GRIN lens represented by the above-mentioned [Math. 2], therefractive index distribution in the radius direction (r) will bereferred to as “N(r)”.

The first lens 11 of this embodiment is designed such that second orderdifferential of the refractive index distribution N(r) in the radiusdirection

$\begin{matrix}\frac{\partial^{2}N}{\partial R^{2}} & \left\lbrack {{Math}.\mspace{14mu} 3} \right\rbrack\end{matrix}$increases monotonically.

Hereinafter, the refractive index distribution N(r) of the first lens 11in the radius direction will be referred to as “N₁(r)”.

Moreover, second order differential of the refractive index distributionN₁(r) of the first lens 11 in the radius direction is represented by thefollowing mathematical formula.

$\begin{matrix}\frac{\partial^{2}N_{1}}{\partial R^{2}} & \left\lbrack {{Math}.\mspace{14mu} 4} \right\rbrack\end{matrix}$Because the refractive index distribution N₁(r) is prepared such thatsecond order differential in the radius direction increasesmonotonically as described above, a spherical-aberration-correctioneffect of the first lens 11 is obtained.Here, FIGS. 3A and 3B show an example of a refractive index distributionpattern in the radius direction to be prepared in order to correctspherical aberration.

The refractive index distribution N(r) of FIG. 3A or FIG. 3B is preparedto obtain a spherical-aberration-correction effect.

It is understood that second order differential of the refractive indexdistribution N(r) of either FIG. 3A or FIG. 3B in the radius directionincreases monotonically.

It means that, the first lens 11, of which second order differential ofthe refractive index distribution N₁(r) in the radius directionincreases monotonically, obtains a spherical-aberration-correctioneffect.

Here, in this embodiment, not only the first lens 11 is a gradient indexlens, but also the second lens 12 is a gradient index lens.

As a result, degree of freedom of design of the second lens 12 per seand degree of freedom of design of the entire optical system may beincreased.

Moreover, in this embodiment, one of the first lens 11 and the secondlens 12 has refractive index distribution also in the optical-axisdirection.

Because of refractive index distribution in the optical-axis direction,degree of freedom of optical design may be further increased.

Here, a below-mentioned example proposes a structure in which both thefirst lens 11 and the second lens 12 have refractive index distributionsalso in the optical-axis direction (Example 3).

If both the first lens 11 and the second lens 12 have refractive indexdistributions also in the optical-axis direction, the relation of secondorder differential of the refractive index distribution N₁ of the firstlens 11 in the optical-axis direction (Z) and second order differentialof the refractive index distribution (hereinafter referred to asrefractive index distribution N₂) of the second lens 12 in theoptical-axis direction is positive/negative. As a result, MTF(Modulation Transfer Function) is improved in a wide angle of view. Inother words, resolution performance is increased.

Here, an example of a condition of the above-mentioned “the relation ofsecond order differential of the refractive index distribution N₁ of thefirst lens 11 in the optical-axis direction and second orderdifferential of the refractive index distribution N₂ of the second lens12 in the optical-axis direction is positive/negative” is for examplethe condition of the following [Math. 5].

$\begin{matrix}{\left. \frac{\partial^{2}N_{1}}{\partial Z^{2}} \middle| {}_{z = {t_{1}/2}}{\geq 0} \right.{and}\left. \frac{\partial^{2}N_{2}}{\partial Z^{2}} \middle| {}_{z = {t_{2}/2}}{\leq 0} \right.} & \left\lbrack {{Math}.\mspace{14mu} 5} \right\rbrack\end{matrix}$where “N₁(r,z)” means the refractive index distribution (radiusdirection and optical-axis direction) of the first lens 11, and“N₂(r,z)” means the refractive index distribution (radius direction andoptical-axis direction) of the second lens 12 in [Math. 5]. Moreover, t₁and t₂ mean the center thickness of the first lens 11 and the centerthickness of the second lens 12, respectively.

If the above-mentioned condition “the relation of second orderdifferential of the refractive index distribution N₁ of the first lens11 in the optical-axis direction and second order differential of therefractive index distribution N₂ of the second lens 12 in theoptical-axis direction is positive/negative” is satisfied, then it meansthat aberration correction at the first lens 11 side and aberrationcorrection at the second lens 12 side are well-balanced. As a result, itis possible to increase an effect of correcting peripheral aberration,and resolution may be increased in a wide angle of view.

Moreover, in this embodiment, a so-called metamaterial lens may be usedas a GRIN lens.

Here, a metamaterial is an artificial structure including unit cells,each of which has a side shorter than the wavelength-in-use. Theabove-mentioned unit cell has an internal conductor, a dielectricmaterial supports the conductor, and the metamaterial is thusstructured.

Each of FIGS. 4A and 4B shows an example of the structure of a unit cell15 of a metamaterial.

As shown in FIG. 4A or FIG. 4B, the unit cell 15 has an internalconductor 16. A dielectric material supports the conductor 16, and theunit cell 15 is thus formed. As shown in FIG. 5, such unit cells 15 arestacked in the X, Y, and Z directions, and a metamaterial (metamateriallens) is thus formed.

Here, a metamaterial controls the structure of the unit cell 15, andutilizes one of or both of electric resonance and magnetic resonanceresulting from an incident wavelength. As a result, the metamaterial iscapable of controlling electric permittivity and magnetic permeabilityof an electromagnetic wave having a wavelength-in-use.

As is known, the square root of the product of electric permittivity (ε)and magnetic permeability (μ) is a refractive index.

Here, a GRIN lens in the past, which does not employ such ametamaterial, is manufactured by for example an ion-exchange method, asol-gel method, or the like, i.e., by using an electromagnetic fieldwhen a material is being solved or is gel-like and by thus controllingthe distribution of metal ions. However, it is difficult for such a GRINlens in the past to form a complicated refractive index distribution.Because of this, it is difficult to obtain refractive index distributioncorresponding to an effect of an aspheric shape.

Moreover, if a device has a refractive index distribution in the radiusdirection, the optical power of the device is determined based on therefractive index difference in the radius direction and based on thelength in the optical-axis direction. It is difficult for a GRIN lens inthe past to obtain a large refractive index difference. As a result, anenough optical power may be obtained only if a GRIN lens in the past hasa smaller diameter and is long along the optical axis.

In other words, as a result, it may be difficult to apply a GRIN lens inthe past to an image-pickup optical system, which requires relativelyhigh brightness, such as the infrared image-pickup optical systemexemplified in this embodiment.

In view of this point, in the below-mentioned examples, a metamateriallens is used as a GRIN lens.

As described above, the square root of the product of electricpermittivity and magnetic permeability is a refractive index of ametamaterial lens. In view of this, it is possible to generate acomplicated refractive index distribution relatively easily by changingthe structures of unit cells depending on positions.

As a result, it is possible to easily realize, by using a metamateriallens, coexistence of refractive index distributions in the radiusdirection and in the optical-axis direction and a complicated refractiveindex distribution, which are difficult to realize by a known method ofmanufacturing a GRIN lens.

In other words, as a result, it is easy to design an image-pickupoptical system having a high aberration correction ability and enablinghigh resolution.

Moreover, because a metamaterial lens is capable of easily realizing alarge refractive index difference, it is easy to make lenses (especiallysecond lens 12 for collecting light) thinner and make the lenses largerin diameter. As a result, it is advantageous to increase in brightnessof the optical system.

Here, when a metamaterial lens is used, it is possible to controlpolarization properties by devising the structure of of the metamateriallens.

For example, as previously shown in FIG. 4A, if the structure of theunit cell 15 has a structure symmetric with respect to three axes, i.e.,the Z axis (optical-axis direction), the X axis, and the Y axis, the Xaxis and the Y axis being on a plane perpendicular to the Z axis, thenthe unit cell 15 has an isotropic refractive index. In other words, theunit cell 15 has the same refractive index with respect to incidentelectromagnetic waves having arbitrary polarization direction.

In general, electromagnetic waves having various polarization directionsenter the image-pickup optical system. The structure of FIG. 4A iscapable of equalizing refractive indexes with respect to those arbitrarypolarization directions.

Alternatively, as shown in FIG. 4B, the structure symmetric with respectto only two axes, i.e., the X axis and the Y axis, may be employed. Inthis case, the refractive index N_(X-Y) of an electromagnetic wavehaving polarization on the X-Y plane is different from the refractiveindex N_(Z) of an electromagnetic wave having polarization in the Z axisdirection.

At this time, an electromagnetic wave entering the X-Y planeperpendicularly, i.e., an electromagnetic wave having polarizationparallel to the X-Y plane, has a refractive index N_(X-Y). Meanwhile, arefractive index of an electromagnetic wave entering the X-Y plane notperpendicularly or an electromagnetic wave entering the X-Y planeperpendicularly but then refracted is determined based on a refractiveindex ellipsoid having N_(X-Y) and N_(Z) and based on a direction vectorof the electromagnetic wave.

It means that different incident angles result in different refractiveindexes even if an electromagnetic wave enters the same position of alens. Especially when an image-pickup optical system having a largeangle of view is designed, this may be one degree of freedom.

It is possible to manufacture a metamaterial lens by using amicrofabrication technology.

For example, a conductor structure is etched on a printed board made ofa dielectric material, whereby the unit cell 15 is structured.Alternatively, it may be manufactured by using a semiconductor process(lithography, vapor deposition, etching, etc.).

Moreover, there is proposed a method including arranging a conductorstructure in a liquid/gel dielectric material and then curing thedielectric material. In this embodiment, a metamaterial lens ismanufactured by using one of those methods, for example.

With reference to FIGS. 6A and 6B, a method of giving a refractive indexdistribution to a metamaterial lens will be specifically described.

In FIGS. 6A and 6B, firstly, it is presupposed that the unit cell 15 inthis case is approximately cubic and that the length m of the side isabout 1 μm.

In this case, the conductor 16 is Cu (copper), and a dielectric materialsupporting the conductor 16 is BaF₂ (barium fluoride).

As described above, BaF₂ supports the Cu structure in the unit cell 15,whereby it is possible to change a refractive index by changing theshape of Cu.

For example, in the example of those figures, the Cu structure has across-shaped structure.

The widths a of the four arms of the cross-shaped Cu are the same (forexample a=180 nm). At this time, it is possible to adjust the refractiveindex depending on the length b of the cross-shaped arms by changing thelength b as shown in FIG. 6A and FIG. 6B.

FIG. 7 shows measurement results of refractive indexes when the length bof the arms is changed.

Specifically, FIG. 7 shows change characteristics of refractive indexeswith respect to wavelength (μm) when the length b of the arms is changedby 100 nm in the range of b=300 nm to 800 nm.

Also with reference to FIG. 7, it is understood that it is possible toadjust the refractive index depending on the length b of the arms.

It is possible for a metamaterial lens to have a refractive indexdistribution by combining the unit cells 15, each of which has arequired refractive index depending on the shape of such a Cu plate(conductor 16), in the stacked product as previously shown in FIG. 5.Specifically, the unit cells 15 stacked in the radius direction iscapable of obtaining a refractive index distribution N(r) in the radiusdirection, and the unit cells 15 stacked in the optical-axis directionis capable of obtaining a refractive index distribution N(z) in theoptical-axis direction.

In the below-mentioned examples, a metamaterial lens having a requiredrefractive index distribution is manufactured by using such a method.

Here, in this embodiment, a metamaterial lens may only be used as thefirst lens 11, or metamaterial lenses may be used as both the first lens11 and the second lens 12. Especially if a metamaterial lens is used asthe second lens 12, the second lens 12 may include a plurality ofmetamaterial lenses instead of one metamaterial lens.

As is understood from the above description, in this embodiment, becauseoptical power is concentrated on the second lens 12 to form an image,the second lens 12 tends to be thick. If conductor structures anddielectric materials are stack to manufacture a metamaterial lens, thelarger the thickness of a lens, the longer the manufacturing time.

In view of this, especially if the second lens 12 consists of a lensgroup including a plurality of metamaterial lenses, the manufacturingtime may be reduced. In other words, because it is possible to make eachone of metamaterial lenses thinner, it is possible to reduce themanufacturing time of each metamaterial lens. If the lenses aremanufactured in parallel, it is possible to greatly reduce themanufacturing time of the second lens 12 compared to the second lens 12consisting of one metamaterial lens.

Note that if a lens group including a plurality of metamaterial lensesis provided as described above, it is desirable that the thickness ofeach metamaterial lens should be 0.2 mm or more from the viewpoint ofretention of strength.

Meanwhile, in recent years, a device using far-infrared is used as atemperature sensor or a motion sensor. However, the resolution of atemperature sensor or a motion sensor is low. A few kinds of devicessuch as thermo viewers and night vision systems include optical systemsconfigured to form an image even of the shape of an object. In thefuture, it is desirable that optical systems should have wider angles ofview in order to use such devices widely for various purposes.Specifically, an optical system, whose angle of view exceeds at least25°, is desirable.

In the below-mentioned specific examples, optical systems are designedin view of this point.

Moreover, because far-infrared light and terahertz waves are low inenergy, it is not possible to use an image sensor for visible light, andsensitivity of the image sensor 3 is relatively low. Because of this, itis desirable that F-number should be high to collect a larger amount oflight, and it is desirable that F-number should be 1.8 or less, forexample.

Moreover, for a purpose such as temperature distribution measurement,which requires resolution, it is desirable that F-number should be 1.3or less in order to increase the amount of collected light and toincrease resolution.

In the below-mentioned specific examples, optical systems are designedalso in view of such requirement of F-number.

2. Specific Examples 2-1. Example 1

FIG. 8 shows the structure of an image-pickup optical system of Example1.

Note that, in FIG. 8, the plane Simg (hereinafter referred to as imagingplane Simg) in this figure shows the imaging plane of the image sensor 3shown in FIG. 1 (and FIG. 2).

Moreover, FIG. 8 also shows infrared light beams (far-infrared light:central wavelength of 10 μm).

In this figure, light beams of the extremely-short-dashed lines showlight beams collected at the image height 0.0 mm, and light beams of theshort-dashed lines show light beams collected at the image height 1.5mm. Further, light beams of the solid lines show light beams collectedat the image height 3.5 mm, and light beams of the long-dashed linesshow light beams collected at the image height 5.0 mm.

In this example, metamaterial lenses are used as both the first lens 11and the second lens 12.

Moreover, in this example, both the first lens 11 and the second lens 12have refractive index distributions only in the radius direction, and donot have refractive index distributions in the optical-axis direction.

Specifically, the coefficients of the first lens 11 and the second lens12 set in this case are as follows.

First lens 11

t₁: 0.51 mm

N₁₀=1.5

nr₁₂=−0.0045619

nr₁₄=2.6341×10⁻⁵

nr₁₆=3.9083×10⁻⁵

nz₁₁=0

nz₁₂=0

nz₁₃=0

Second lens 12

t₂: 20.98 mm

N₂₀=1.7

nr₂₂=−0.0014226

nr₂₄=1.5207×10⁻⁷

nr₂₆=−2.4759×10⁻¹⁰

nz₁₁=0

nz₁₂=0

nz₁₃=0

Note that t₁ and t₂ are the center thicknesses of the first lens 11 andthe second lens 12, respectively.

Moreover, N₂₀ is the standard refractive index of the second lens 12.

The structure of the image-pickup optical system is as follows. Thedistance between an object and the aperture stop 10 is 9000 mm, thedistance between the aperture stop 10 and the first lens 11 is 0 mm, thedistance between the first lens 11 and the second lens 12 is 12.27 mm,the distance between the second lens 12 and the sensor window 13 is 9.60mm, and the distance between the sensor window 13 and the imaging planeSimg is 0.95 mm.

The thickness of the sensor window 13 is 1.0 mm, the sensor window 13 ismade of Si (silicon), and the refractive index of the sensor window 13with respect to the wavelength of 10 μm is 3.42.

The focal distance f of the entire optical system is 19 mm, the diameterof the aperture stop 10 is 18.1 mm, and F-number=1.06 and the horizontalangle of view of 23.8 degrees are realized.

Here, the value of second order differential of the refractive indexdistribution N₁ of the first lens 11 with the radius direction positionR is represented by the following formula.

$\begin{matrix}{\frac{\partial^{2}N_{1}}{\partial R^{2}} = {{2 \cdot {nr}_{12}} + {12 \cdot {nr}_{14} \cdot R^{2}} + {30 \cdot {nr}_{15} \cdot R^{4}}}} & \left\lbrack {{Math}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

In Example 1, because the values nr₁₄ and nr₁₆ are positive, as shown inthe graph of FIG. 9, in this case, second order differential of therefractive index distribution N₁ in the radius direction increasesmonotonically (increase monotonically with respect to increase in R).

Moreover, the focal distance f₂ of the second lens 12 alone is obtainedbased on the following formula, which is derived from the formula of thefocal distance of a GRIN lens, where nr₂₂ is negative.

$\begin{matrix}{f_{2} = \frac{1}{\sqrt{{2 \cdot N_{20} \cdot {nr}_{22}}} \cdot {\sin\left( {t_{2} \cdot {\frac{2 \cdot {nr}_{22}}{N_{20}}}^{1/2}} \right)}}} & \left\lbrack {{Math}.\mspace{14mu} 7} \right\rbrack\end{matrix}$The focal distance f₂ of Example 1 is calculated based on [Math. 7] andbased on the coefficient nr₂₂=−0.0014226 set for the second lens 12 inthis case, and is 19.0. As a result, f₂/f=1.0 is established, and theabove-mentioned condition “0.9≤f₂/f≤1.1” is satisfied. In other words,it means that aberration (comatic aberration and astigmatic aberration)is reduced in this structure.

FIG. 10 shows resolution properties (MTFs) of the image-pickup opticalsystem of Example 1 at the respective image heights (0.0 mm, 1.5 mm, and3.5 mm).

Note that in FIG. 10 and in addition the following MTF diagrams (FIGS.13, 18, 21, and 24), commonly, the extremely-short-dashed lines in thosefigures show the properties at the image height 0.0 mm, the short-dashedlines show the properties at the image height 1.5 mm, and the solidlines show the properties at the image height 3.5 mm. Moreover, in thosefigures, “T” means tangential values, and “S” means sagittal values.

Here, it is desirable that the MTF value of 20 line pairs/mm at theimage height 0.0 mm, i.e., 0%, should be 0.3 or more, that the MTF valueof 20 line pairs/mm at the image height 1.5 mm, i.e., 30%, should be 0.3or more, and that the MTF value of 10 line pairs/mm at the image height3.5 mm, i.e., 70%, should be 0.3 or more, where the image height 5.0 mmis 100%.

In this example, because of the above-mentioned design, high resolutionis obtained, in which the MTF values (tangential and sagittal) of 20line pairs/mm at the image height 0.0 mm are 0.688, the MTF tangentialvalue and sagittal value of 20 line pairs/mm at the image height 1.5 mmare 0.621 and 0.631, and the MTF tangential value and sagittal value of10 line pairs/mm at the image height 3.5 mm are 0.661 and 0.482.

According to the above-mentioned Example 1, since two GRIN lenses areused, it is possible to reduce various kinds of aberration such asspherical aberration, comatic aberration, and astigmatic aberration, andto obtain a high-resolution image while the number of lenses is reduced.

Moreover, because GRIN lenses are made of metamaterials, it is possibleto realize lenses each having a higher-order refractive indexdistribution and refractive index distributions in the radius directionand the optical-axis direction, and it is possible to structure anoptical system having a small F-number and a wide angle of view, furtherin view of the polarization direction of incident light.

2-2. Example 2

FIG. 11 shows the structure of an image-pickup optical system of Example2.

Note that similarly FIG. 11 also shows infrared light beams collected atthe respective image heights (0.0 mm, 1.5 mm, 3.5 mm, and 5.0 mm). Alsoin this case, the extremely-short-dashed lines show the image height 0.0mm, the short-dashed lines show the image height 1.5 mm, the solid linesshow the image height 3.5 mm, and the long-dashed lines show the imageheight 5.0 mm.

Also in the image-pickup optical system of Example 2 shown in FIG. 11,metamaterial lenses are used as both the first lens 11 and the secondlens 12.

In Example 2, the first lens 11 has a refractive index distribution onlyin the radius direction, and the second lens 12 has a refractive indexdistribution in both the radius direction and the optical-axisdirection.

The coefficients of the first lens 11 and the second lens 12 of Example2 are as follows.

First lens 11

t₁: 1.45 mm

N₁₀=1.5

nr₁₂=−0.0026979

nr₁4=8.3000×10⁻⁸

nr₁₆=1.3708×10⁻⁸

nz₁₁=0

nz₁₂=0

nz₁₃=0

Second lens 12

t₂: 22.1 mm

N₂₀=1.7

nr₂₂=−0.0012917

nr₂₄=6.0592×10⁻⁸

nr₂₆=−1.0504×10⁻¹⁰

nz₁₁=0.18715

nz₁₂=−0.010492

nz₁₃=0.00016204

Also in Example 2, the distance between an object and the aperture stop10 is 9000 mm, and the distance between the aperture stop 10 and thefirst lens 11 is 0 mm. In this case, the distance between the first lens11 and the second lens 12 is 13.47 mm, the distance between the secondlens 12 and the sensor window 13 is 10.54 mm, and the distance betweenthe sensor window 13 and the imaging plane Simg is 0.95 mm.

Also in Example 2, the thickness of the sensor window 13 is 1.0 mm, thesensor window 13 is made of Si, and the refractive index of the sensorwindow 13 with respect to the wavelength of 10 μm is 3.42.

Also in this case, the focal distance f of the entire optical system is19 mm, the diameter of the aperture stop 10 is 18.1 mm, andF-number=1.06 and the horizontal angle of view of 23.8 degrees arerealized.

Also according to the optical system of Example 2, the value of secondorder differential of the refractive index distribution N₁ of the firstlens 11 with the radius direction position R increases monotonically.

In other words, also in Example 2, because the values nr₁₄ and nr₁₆ arepositive, as shown in the graph of FIG. 12, second order differential ofthe refractive index distribution N₁ of the first lens 11 in the radiusdirection increases monotonically with respect to increase in R.

Moreover, in Example 2, the focal distance f₂ of the second lens 12alone is calculated based on nr₂₂=−0.0012917 set in this case and basedon the previous [Math. 7], and is 19.88. As a result, f₂/f=1.05 isestablished.

In other words, also according to the structure in this case, thecondition “0.9≤f₂/f≤1.1” is satisfied, and comatic aberration andastigmatic aberration are reduced.

FIG. 13 shows resolution properties (MTFs) of the image-pickup opticalsystem of Example 2 at the respective image heights (0.0 mm, 1.5 mm, and3.5 mm).

In Example 2, high resolution is obtained, in which the MTF values(tangential and sagittal) of 20 line pairs/mm at the image height 0.0 mmare 0.687, the MTF tangential value and sagittal value of 20 linepairs/mm at the image height 1.5 mm are 0.664 and 0.715, and the MTFtangential value and sagittal value of 10 line pairs/mm at the imageheight 3.5 mm are 0.824 and 0.781.

Also according to the above-mentioned Example 2, since two GRIN lensesare used, it is possible to reduce various kinds of aberration such asspherical aberration, comatic aberration, and astigmatic aberration, andto obtain a high-resolution image while the number of lenses is reduced.Moreover, because metamaterial lenses are used as GRIN lenses, it ispossible to realize lenses each having a higher-order refractive indexdistribution and refractive index distributions in the radius directionand the optical-axis direction, and it is possible to structure anoptical system having a small F-number and a wide angle of view, furtherin view of the polarization direction of incident light.

2-3. Example 3

FIG. 14 shows the structure of an image-pickup optical system of Example3.

Note that similarly FIG. 13 also shows infrared light beams collected atthe respective image heights (0.0 mm, 1.5 mm, 3.5 mm, and 5.0 mm). Alsoin this case, the extremely-short-dashed lines show the image height 0.0mm, the short-dashed lines show the image height 1.5 mm, the solid linesshow the image height 3.5 mm, and the long-dashed lines show the imageheight 5.0 mm.

Also in the image-pickup optical system of Example 3 shown in FIG. 14,metamaterial lenses are used as both the first lens 11 and the secondlens 12. In Example 3, both the first lens 11 and the second lens 12have refractive index distributions in both the radius direction and theoptical-axis direction.

The coefficients of the first lens 11 and the second lens 12 of Example3 are as follows.

First lens 11

t₁: 0.32 mm

N₁₀=1.5

nr₁₂=−0.0084099

nr₁₄=4.5915×10⁻⁵

nr₁₆=2.3249×10⁻⁸

nz₁₁=11.279

nz₁₂=54.660

nz₁₃=−53.038

Second lens 12

t₂: 21.59 mm

N₂₀=1.7

nr₂₂=−0.0013365

nr₂₄=1.0580×10⁻⁷

nr₂₆=−2.0880×10⁻¹⁰

nz₁₁=0.16587

nz₁₂=−0.011007

nz₁₃=0.00013715

Also in Example 3, the distance between an object and the aperture stop10 is 9000 mm, and the distance between the aperture stop and the firstlens 11 is 0 mm. In this case, the distance between the first lens 11and the second lens 12 is 13.06 mm, the distance between the second lens12 and the sensor window 13 is 10.38 mm, and the distance between thesensor window 13 and the imaging plane Simg is 0.95 mm.

Also in this case, the thickness of the sensor window 13 is 1.0 mm, thesensor window 13 is made of Si, and the refractive index of the sensorwindow 13 with respect to the wavelength of 10 μm is 3.42.

Also in this example, the focal distance f of the entire optical systemis 19 mm, the diameter of the aperture stop 10 is 18.1 mm, andF-number=1.06 and the horizontal angle of view of 23.8 degrees arerealized.

Also according to Example 3, the value of second order differential ofthe refractive index distribution N₁ of the first lens 11 with theradius direction position R increases monotonically.

In other words, also in this case, because the values nr₁₄ and nr₁₆ arepositive, as shown in the graph of FIG. 15, second order differential ofthe refractive index distribution N₁ in the radius direction increasesmonotonically with respect to increase in R.

Moreover, in Example 3, the focal distance f₂ of the second lens 12alone is calculated based on nr₂₂=−0.0013365 and based on the previous[Math. 7], and is 19.64. As a result, f₂/f=1.03 is established.

In other words, also in this case, “0.9≤f₂/f_(1.1)” is satisfied, andcomatic aberration and astigmatic aberration are reduced.

Here, in Example 3, both the first lens 11 and the second lens 12 haverefractive index distributions in both the radius direction and theoptical-axis direction.

Second order differential of the refractive index distribution N₁ of thefirst lens 11 at a position Z in the optical-axis direction is asfollows.

$\begin{matrix}{\frac{\partial^{2}N_{1}}{\partial Z^{2}} = {{2 \cdot {nz}_{12}} + {6 \cdot {nz}_{13} \cdot Z}}} & \left\lbrack {{Math}.\mspace{14mu} 8} \right\rbrack\end{matrix}$

FIG. 16 shows the graph of the above-mentioned [Math. 8]. As shown inFIG. 16, [Math. 8] is always positive within the range Z=0 to 0.32 mm ofthe thickness of the first lens 11.

Meanwhile, second order differential of the refractive indexdistribution N₂ of the second lens 12 at the position Z in theoptical-axis direction is as follows.

$\begin{matrix}{\frac{\partial^{2}N_{2}}{\partial Z^{2}} = {{2 \cdot {nz}_{22}} + {6 \cdot {nz}_{23} \cdot Z}}} & \left\lbrack {{Math}.\mspace{14mu} 9} \right\rbrack\end{matrix}$

FIG. 17 shows the graph of the above-mentioned [Math. 9]. As shown inFIG. 17, [Math. 9] is always negative within the range Z=0 to 21.59 mmof the thickness of the second lens 12.

As a result, the above-mentioned [Math. 8] is positive where z=t₁/2, andthe above-mentioned [Math. 9] is negative where z=t₂/2.

In other words, in Example 3, the above-mentioned condition “therelation of second order differential of the refractive indexdistribution N₁ of the first lens 11 in the optical-axis direction andsecond order differential of the refractive index distribution N₂ of thesecond lens 12 in the optical-axis direction is positive/negative” issatisfied.

FIG. 18 shows resolution properties (MTFs) of the image-pickup opticalsystem of Example 3 at the respective image heights (0.0 mm, 1.5 mm, and3.5 mm).

In Example 3, high resolution is obtained, in which the MTF values(tangential and sagittal) of 20 line pairs/mm at the image height 0.0 mmare 0.718, the MTF tangential value and sagittal value of 20 linepairs/mm at the image height 1.5 mm are 0.655 and 0.658, and the MTFtangential value and sagittal value of 10 line pairs/mm at the imageheight 3.5 mm are 0.692 and 0.707.

Also according to Example 3, since two GRIN lenses are used, it ispossible to reduce various kinds of aberration such as sphericalaberration, comatic aberration, and astigmatic aberration, and to obtaina high-resolution image while the number of lenses is reduced. Moreover,because metamaterial lenses are used as GRIN lenses, it is possible torealize lenses each having a higher-order refractive index distributionand refractive index distributions in the radius direction and theoptical-axis direction, and it is possible to structure an opticalsystem having a small F-number and a wide angle of view, further in viewof the polarization direction of incident light.

2-4. Example 4

FIG. 19 shows the structure of an image-pickup optical system of Example4.

Note that similarly FIG. 19 also shows infrared light beams collected atthe respective image heights (0.0 mm, 1.5 mm, 3.5 mm, and 5.0 mm). Alsoin this case, the extremely-short-dashed lines show the image height 0.0mm, the short-dashed lines show the image height 1.5 mm, the solid linesshow the image height 3.5 mm, and the long-dashed lines show the imageheight 5.0 mm.

Also in the image-pickup optical system of Example 4, metamateriallenses are used as both the first lens 11 and the second lens 12.

As shown in the figure, in Example 4, the second lens 12 consists of aplurality of metamaterial lenses 12 a.

Specifically, in this case, twenty metamaterial lenses 12 a are arrayedin the optical-axis direction at regular intervals, whereby the secondlens 12 is structured. In this example, the interval between themetamaterial lenses 12 a is 0.2 mm.

In Example 4, similar to the above-mentioned Example 2, both the firstlens 11 and the second lens 12 have refractive index distributions inthe radius direction, and only the second lens 12 has a refractive indexdistribution in the optical-axis direction.

The coefficients of the first lens 11 and the second lens 12 of Example4 are as follows.

First lens 11

t₁: 1.0 mm

N₁₀=1.5

nr₁₂=−0.0030892

nr₁₄=1.4311×10⁻⁸

nr₁₆=1.7893×10⁻⁸

nz₁₁=0.0

nz₁₂=0.0

nz₁₃=0.0

Each metamaterial lens 12 a of second lens 12

t₂: 1.0 mm

N₂₀=1.7

nr₂₂=−0.0014303404

nr₂₄=6.8750×10⁻⁸

nr₂₆=−9.9276×10⁻¹¹

nz₁₁=21.915

nz₁₂=−13.609

nz₁₃=4.3708

For confirmation, in this case, the above-mentioned t₂ shows the centerthickness of one metamaterial lens 12 a.

Here, as is understood based on the above-mentioned set values, in thisexample, the lenses 12 a of the second lens 12 are designed in the samemanner. Because the lenses are designed in the same manner as describedabove, the manufacturing efficiency may be increased, and as a resultthe costs may be reduced.

Further, in this example, the thickness of the first lens 11 is the sameas the thickness of each metamaterial lens 12 a of the second lens 12,and the thickness of them is 1.0 mm. As a result, if there is employedthe above-mentioned method of stacking the unit cell structures tomanufacture a metamaterial lens, it is possible to manufacture each lensefficiently.

Also in Example 4, the distance between an object and the aperture stop10 is 9000 mm, and the distance between the aperture stop 10 and thefirst lens 11 is 0 mm. In this case, the distance between the first lens11 and the second lens 12 is 15.22 mm, the distance between the secondlens 12 and the sensor window 13 is 11.85 mm, and the distance betweenthe sensor window 13 and the imaging plane Simg is 0.95 mm.

Also in this case, the thickness of the sensor window 13 is 1.0 mm, thesensor window 13 is made of Si, and the refractive index of the sensorwindow 13 with respect to the wavelength of 10 μm is 3.42.

In this case, the focal distance f of the entire optical system is 18.64mm, and the diameter of the aperture stop 10 is 17.75 mm.

In Example 4, F-number=1.05 and the horizontal angle of view of 24.2degrees are realized.

In Example 4, because the values nr₁₄ and nr₁₆ are positive also in thiscase, as shown in the graph of FIG. 20, second order differential of therefractive index distribution N₁ of the first lens 11 in the radiusdirection position R increases monotonically with respect to increase inR.

Moreover, in this case, the focal distance f₂ of the second lens 12 is18.60 mm. In this example, because the focal distance f of the entireoptical system is 18.64 mm, f₂/f=0.998 is established.

In other words, also according to the structure in this case, thecondition “0.9≤f₂/f≤1.1” is satisfied, and comatic aberration andastigmatic aberration are reduced.

FIG. 21 shows resolution properties (MTFs) of the image-pickup opticalsystem of Example 4 at the respective image heights (0.0 mm, 1.5 mm, and3.5 mm).

In Example 4, high resolution is obtained, in which the MTF values(tangential and sagittal) of 20 line pairs/mm at the image height 0.0 mmare 0.727, the MTF tangential value and sagittal value of 20 linepairs/mm at the image height 1.5 mm are 0.695 and 0.719, and the MTFtangential value and sagittal value of 10 line pairs/mm at the imageheight 3.5 mm are 0.811 and 0.852.

Also according to Example 4, since GRIN lenses are used, it is possibleto reduce various kinds of aberration such as spherical aberration,comatic aberration, and astigmatic aberration, and to obtain ahigh-resolution image. Moreover, also in this case, because metamateriallenses are used as GRIN lenses, it is possible to realize lenses eachhaving a higher-order refractive index distribution and refractive indexdistributions in the radius direction and the optical-axis direction,and it is possible to structure an optical system having a smallF-number and a wide angle of view, further in view of the polarizationdirection of incident light.

Meanwhile, in Example 4, the metamaterial lenses 12 a of the second lens12 may be arranged without intervals.

In this case, it is sometimes difficult to closely-attach the lenses 12a without gaps because of, for example, variations of the flatness ofthe lenses 12 a, or the like. If there are unnecessary gaps between thelenses 12 a, optical interference may occur. In view of this, it isdesirable to arrange the lenses 12 a at predetermined intervals.

Here, if the lenses 12 a of the second lens 12 are arranged atpredetermined intervals, reflection will occur at the gaps between thelenses 12 a because of the difference of the refractive index of thelenses 12 a and the refractive index of air. It is desirable that thelenses 12 a should be anti-reflective in order to reduce optical lossresulting from such reflection.

For example, a method of forming anti-reflective films on the bothsurfaces of each metamaterial lens 12 a, or the like may be employed.

Alternatively, the structure of the metamaterial lenses 12 a may bedevised to realize anti-reflection instead of forming anti-reflectivefilms.

Here, the ratio of the electric permittivity and the magneticpermeability of the unit cell 15 of the metamaterial lens 12 a isadjusted without changing the product of the electric permittivity andthe magnetic permeability, whereby the impedance of the unit cell 15 maybe the same as the impedance of the adjacent substance and therefractive index of the unit cell 15 may be different from therefractive index of the adjacent substance at the same time. It ispossible to reduce reflection at the interfaces of the metamateriallenses 12 a and air by using such properties.

Specifically, if the unit cell 15 is structured such that the electricpermittivity ε is equal to the magnetic permeability μ, the impedanceZ=(μ/ε)½=1 is established while the refractive index n=(εμ)½ isadjusted. It is possible to reduce fresnel reflection at the interfacesof the metamaterial lenses 12 a and air.

Note that the first lens 11 may also employ the structure in which thestructure of a metamaterial lens itself provides an anti-reflectiveeffect. Moreover, even if the second lens 12 consists of onemetamaterial lens as previously described in Example 1 or the like, themetamaterial lens may employ such a structure.

2-5. Example 5

FIG. 22 shows the structure of an image-pickup optical system of Example5.

Note that similarly FIG. 22 also shows infrared light beams collected atthe respective image heights (0.0 mm, 1.5 mm, 3.5 mm, and 5.0 mm). Alsoin this case, the extremely-short-dashed lines show the image height 0.0mm, the short-dashed lines show the image height 1.5 mm, the solid linesshow the image height 3.5 mm, and the long-dashed lines show the imageheight 5.0 mm.

As shown in FIG. 22, in the image-pickup optical system of Example 5,similar to the above-mentioned Examples 1 to 3, the first lens 11consists of one lens and the second lens 12 consists of one lens.

Also in this case, metamaterial lenses are used as both the first lens11 and the second lens 12.

Moreover, in Example 5, similar to the above-mentioned Example 1, boththe first lens 11 and the second lens 12 have refractive indexdistributions only in the radius direction.

In Example 5, chromatic aberration may be reduced especially based onthe following design.

The coefficients of the first lens 11 and the second lens 12 set inExample 5 are as follows.

First lens 11

t₁: 0.4 mm

N₁₀=1.5

nr₁₂=−0.011

nr₁₄=3.2962×10⁻⁵

nr₁₆=4.3911×10⁻⁵

nz₁₁=0

nz₁₂=0

nz₁₃=0

Second lens 12

t₂: 16.07 mm

N₂₀=1.7

nr₂₂=−0.0018027

nr₂₄=2.5702×10⁻⁷

nr₂₆=−3.7334×10⁻¹⁰

nz₁₁=0

nz₁₂=0

nz₁₃=0

Moreover, also in Example 5, the distance between an object and theaperture stop 10 is 9000 mm, and the distance between the aperture stop10 and the first lens 11 is 0 mm.

In this case, the distance between the first lens 10 and the second lens12 is 14.2 mm, the distance between the second lens 12 and the sensorwindow 13 is 9.65 mm, and the distance between the sensor window 13 andthe imaging plane Simg is 0.95 mm.

Also in this case, the thickness of the sensor window 13 is 1.0 mm, thesensor window 13 is made of Si, and the refractive index of the sensorwindow 13 with respect to the wavelength of 10 μm is 3.42.

In this example, the focal distance f of the entire optical system is 19mm, the diameter of the aperture stop 10 is 18.1 mm, and F-number=1.06and the horizontal angle of view of 23.8 degrees are realized.

Also according to the optical system of Example 5, the value of secondorder differential of the refractive index distribution N₁ of the firstlens 11 with the radius direction position R increases monotonically. Inother words, also in Example 5, because the values nr₁₄ and nr₁₆ arepositive, as shown in the graph of FIG. 23, second order differential ofthe refractive index distribution N₁ of the first lens 11 in the radiusdirection increases monotonically with respect to increase in R.

Moreover, in Example 5, the focal distance f₂ of the second lens 12alone is calculated based on nr₂₂=−0.0018027 set in this case and basedon the previous [Math. 7], and is 18.94. As a result, in this case,f₂/f=1.003 is established, the condition “0.9≤f₂/f≤1.1” is satisfied,and comatic aberration and astigmatic aberration are reduced. FIG. 24shows resolution properties (MTFs) of the image-pickup optical system ofExample 5 at the respective image heights (0.0 mm, 1.5 mm, and 3.5 mm).

In Example 5, high resolution is obtained, in which the MTF values(tangential and sagittal) of 20 line pairs/mm at the image height 0.0 mmare 0.676, the MTF tangential value and sagittal value of 20 linepairs/mm at the image height 1.5 mm are 0.583 and 0.667, and the MTFtangential value and sagittal value of 10 line pairs/mm at the imageheight 3.5 mm are 0.588 and 0.475.

Also according to Example 5, since two GRIN lenses are used, it ispossible to reduce various kinds of aberration such as sphericalaberration, comatic aberration, and astigmatic aberration, and to obtaina high-resolution image while the number of lenses is reduced.

Moreover, also in this case, because metamaterial lenses are used asGRIN lenses, it is possible to realize lenses each having a higher-orderrefractive index distribution and refractive index distributions in theradius direction and the optical-axis direction, and it is possible tostructure an optical system having a small F-number and a wide angle ofview, further in view of the polarization direction of incident light.

Here, according to the above-mentioned Examples, as described above,because the focal distance f₂ of the second lens 12 satisfies thecondition “0.9≤f₂/f≤1.1”, the coefficient nr₁₂, which determines thelight-collecting power of the first lens 11, is approximately 0.

However, if the coefficient nr₁₂ is smaller than 0, chromatic aberrationmay be reduced.

It is known that it is desirable that a material having smallerchromatic dispersion should be used to reduce chromatic aberration.Let's assume a case where a metamaterial substance having refractiveindex change characteristics previously shown in FIG. 7 is used, such asfor example metamaterial lenses used in Examples.

In FIG. 7, in the metamaterial substance, a structural portion, whichhas a refractive index of 1.5 with respect to a wavelength of 10 μm, hasa refractive index of 1.4701 with respect to a wavelength of 12 μm.Moreover, a structural portion, which has a refractive index of 1.7 withrespect to a wavelength of 10 μm, has a refractive index of 1.6599 withrespect to a wavelength of 12 μm.

At this time, in Example 1 where nr₁₂ is −0.0045619, the chromaticaberration is 0.88 mm. Meanwhile, in Example 5 where nr₁₂ is −0.011, thechromatic aberration is 0.82 mm, and the chromatic aberration isimproved.

It is understood from the above that design, with which chromaticaberration is reduced, may be enabled by using a material or ametamaterial substance having a smaller chromatic dispersion to obtainnr₁₂ smaller than 0.

Note that, with only regard to nr₁₂, it is necessary to at least satisfy“nr₁₂<0” to obtain an effect of reducing chromatic aberration.

3. Modification Examples

The image-pickup optical system and the image pickup apparatus of theembodiment of the present technology have been described. The presenttechnology is not limited to the above-mentioned specific examples.

For example, in the illustrated Examples, the present technology is usedto pick up infrared images (wavelength of about 8 μm to 12 μm).Alternatively, the present technology may be used to pick upterahertz-wave images.

A terahertz-wave image-pickup optical system may have a structure inwhich for example an object-of-imaging is irradiated with laser light, aterahertz wave is thus generated, and the generated terahertz waveenters via the aperture stop 10. The structures of the aperture stop 10and thereafter may be similar to the above-mentioned structure. Further,a sensor sensitive to terahertz waves may be used as the image sensor 3.

Moreover, in the above illustration, the distance between the aperturestop 10 and the first lens 11 is 0. The first lens 11 may be arranged asclose to the aperture stop 10 as possible to improve aspherical-aberration-correction effect.

Moreover, in the above illustration of Example 4, when the second lens12 consists of the plurality of metamaterial lenses 12 a, the lenses 12a have the same design without fail. Alternatively, as a matter ofcourse, it is also possible to use differently-designed lenses, or tocombine lenses having one design and lenses having other design.Moreover, the present technology may employ the following structures.

(1) An image-pickup optical system, comprising:

a first lens provided near an aperture stop and configured to correctaberration; and

a second lens arranged between the first lens and an image sensor andconfigured to collect light, wherein

the first lens is a gradient index lens.

(2) The image-pickup optical system according to (1), wherein a focaldistance of the second lens is approximately the same as a focaldistance of the entire image-pickup optical system.

(3) The image-pickup optical system according to (2), wherein

the first lens is designed such that second order differential of arefractive index distribution of the first lens in a radius directionincreases monotonically.

(4) The image-pickup optical system according to (3), wherein the secondlens is a gradient index lens.

(5) The image-pickup optical system according to (4), wherein the firstlens or the second lens has a refractive index distribution in anoptical-axis direction.

(6) The image-pickup optical system according to (4), wherein

both the first lens and the second lens have refractive indexdistributions in an optical-axis direction, and

are designed such that the relation of second order differential of therefractive index distribution of the first lens in the optical-axisdirection and second order differential of the refractive indexdistribution of the second lens in the optical-axis direction ispositive/negative.

(7) The image-pickup optical system according to any one of (4) to (6),wherein

one of the first lens and the second lens is a metamaterial lens.

(8) The image-pickup optical system according to (7), wherein

the metamaterial lens is structured such that refractive indexes inarbitrary polarization directions perpendicular to an optical axis areconstant at an arbitrary point of the metamaterial lens.

(9) The image-pickup optical system according to (7), wherein

the metamaterial lens is structured such that refractive indexes inarbitrary polarization directions are constant at an arbitrary point ofthe metamaterial lens.

(10) The image-pickup optical system according to any one of (7) to (9),wherein the second lens consists of a plurality of metamaterial lenses.

(11) The image-pickup optical system according to (10), wherein

the metamaterial lenses of the second lens are arrayed at predeterminedintervals.

(12) The image-pickup optical system according to any one of (1) to(11), whereinN=N ₀ +nr ₁₂ ·R ² +nr ₁₄ ·R ⁴ +nr ₁₆ ·R ⁶ +nz ₁₁ ·Z+nz ₁₁ ·Z+nz ₁₂ ·Z ²+nz ₁₂ ·Z ³  [Math. 2]is established when a refractive index distribution of the first lens is

$\begin{matrix}{0.9 \leq \frac{f_{2}}{f} \leq 1.1} & \left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack\end{matrix}$

where r is a radius direction position, z is a position in anoptical-axis direction, N₁₀ is a standard refractive index of the firstlens, nr_(1j) is a coefficient of a term r^(j) of a refractive indexdistribution formula, nz_(1k) is a coefficient of a term z^(k) of therefractive index distribution formula, j is an even number, and k is aninteger number.

(13) The image-pickup optical system according to any one of (1) to(12), wherein an infrared image is formed.

(14) The image-pickup optical system according to any one of (1) to(12), wherein a terahertz-wave image is formed.

DESCRIPTION OF SYMBOLS

-   1 image pickup apparatus-   2 optical block-   3 image sensor-   4 image-signal obtaining unit-   5 image signal processor-   10 aperture stop-   11 first lens-   12 second lens-   13 sensor window-   15 unit cell-   16 conductor-   Simg imaging plane

The invention claimed is:
 1. An image-pickup optical system, comprising:an image sensor; an aperture stop; a first lens adjacent to the aperturestop, wherein the first lens is configured to correct aberration; and asecond lens between the first lens and the image sensor, wherein boththe first lens and the second lens have refractive index distributionsin an optical-axis direction, second order differential of a refractiveindex distribution of the first lens in the optical-axis direction ispositive and second order differential of a refractive indexdistribution of the second lens in the optical-axis direction isnegative, and a ratio of a focal distance f₂ of the second lens to afocal distance f of the image-pickup optical system satisfies thefollowing:0.9≤f ₂ /f≤1.1.
 2. The image-pickup optical system according to claim 1,wherein the image sensor is configured to collect light.
 3. Theimage-pickup optical system according to claim 1, wherein the first lensis a gradient index lens.
 4. The image-pickup optical system accordingto claim 3, wherein the second order differential of the refractiveindex distribution of the first lens increases monotonically in a radiusdirection of the first lens.
 5. The image-pickup optical systemaccording to claim 1, wherein the second lens is a gradient index lens.6. The image-pickup optical system according to claim 1, wherein one ofthe first lens or the second lens is a metamaterial lens.
 7. Theimage-pickup optical system according to claim 6, wherein refractiveindexes of the metamaterial lens in arbitrary polarization directionsperpendicular to an optical axis are constant at an arbitrary point ofthe metamaterial lens.
 8. The image-pickup optical system according toclaim 6, wherein refractive indexes of the metamaterial lens inarbitrary polarization directions are constant at an arbitrary point ofthe metamaterial lens.
 9. The image-pickup optical system according toclaim 8, wherein the second lens consists of a plurality of metamateriallenses.
 10. The image-pickup optical system according to claim 8,wherein a plurality of metamaterial lenses of the second lens is arrayedat specific intervals.
 11. The image-pickup optical system according toclaim 1, wherein the first lens is a gradient index lens, and therefractive index distribution N of the first lens is equal to:(N=N₀+nr₁₂ R₂+nr₁₄ R₄+nr₁₆ R₆+nz₁₁ Z+nz₁₂ Z₂+nz₁₃ Z₃) where N₀ is astandard refractive index of the gradient index lens, Z is a position ofthe gradient index lens in the optical-axis direction, R is a positionof the gradient index lens in a radius direction of the gradient indexlens, nr_(1j) is a coefficient of a term R_(j) of a refractive indexdistribution formula, nz_(1k) is a coefficient of a term Z_(k) of therefractive index distribution formula, j is an even number, and k is aninteger number.
 12. The image-pickup optical system according to claim1, wherein the image-pickup optical system is configured to generate aninfrared image.
 13. The image-pickup optical system according to claim1, wherein the image-pickup optical system is configured to generate aterahertz-wave image.
 14. An image-pickup optical system, comprising: animage sensor; an aperture stop; a first lens adjacent to the aperturestop, wherein the first lens is configured to correct aberration, thefirst lens is a gradient index lens, and second order differential of arefractive index distribution of the first lens increases monotonicallyin a radius direction of the first lens; and a second lens between thefirst lens and the image sensor, wherein a ratio of a focal distance f₂of the second lens to a focal distance f of the image-pickup opticalsystem satisfies the following:0.9≤f ₂ /f≤1.1.
 15. An image-pickup optical system, comprising: an imagesensor; an aperture stop; a first lens adjacent to the aperture stop,wherein the first lens is configured to correct aberration; and a secondlens between the first lens and the image sensor, wherein one of thefirst lens or the second lens is a metamaterial lens, refractive indexesof the metamaterial lens in arbitrary polarization directions areconstant at an arbitrary point of the metamaterial lens, and a ratio ofa focal distance f₂ of the second lens to a focal distance f of theimage-pickup optical system satisfies the following:0.9≤f ₂ /f≤1.1.